The Hawking-Page phase transition found a deep interpretation as confinement/deconfinement phase transition in the AdS/CFT conjecture context [1]}, [2]}. While it can also be expressed as a solid/liquid phase transition within the black chemistry [3]}, in which the cosmological constant (anti-de Sitter radius \(\ell \) ) can be identified with the thermodynamic pressure in \(d\) -dimensional spacetime such as [4]}, [5]} :
\(P=-\frac{\Lambda }{8\pi }=\frac{(d-1)(d-2)}{16\pi \ell ^2}.\) 
